Compare modes, ranges and distribution shapes; critique claims and plan fair data collection.
Example 1
Ratings run from 1= very dissatisfied to 5= very satisfied. Which comparison best describes the two distributions?
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Answer: A is concentrated at higher ratings; B is concentrated at lower ratings.
- Satisfaction ratings are ordinal categories with a meaningful order.
- A has most responses at 4 and 5; B has most at 1 and 2. The distribution for A is shifted toward greater satisfaction.
Example 2
A class surveyed all its 19 students: 13 preferred starting sport before lunch and 6 preferred after lunch. Which statement is supported by this investigation?
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Answer: More students in this class preferred sport before lunch.
- 13 is greater than 6, so before lunch was preferred more often in the surveyed class.
- The evidence concerns this class's preferences. It does not establish results for every class or a causal effect on performance.
Example 3
A school newsletter claims “Most students want more football.” Its evidence is a survey of only the football club. What is the main weakness?
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Answer: The surveyed group may not represent all students.
- Football club members are likely to have different interests from some other students.
- To make a school-wide claim, collect relevant responses from a sample that better represents the whole school.